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 Department: Department of Mathematics
Complemented Subspaces of Bounded Linear Operators

Complemented Subspaces of Bounded Linear Operators

Date: August 2003
Creator: Bahreini Esfahani, Manijeh
Description: For many years mathematicians have been interested in the problem of whether an operator ideal is complemented in the space of all bounded linear operators. In this dissertation the complementation of various classes of operators in the space of all bounded linear operators is considered. This paper begins with a preliminary discussion of linear bounded operators as well as operator ideals. Let L(X, Y ) be a Banach space of all bounded linear operator between Banach spaces X and Y , K(X, Y ) be the space of all compact operators, and W(X, Y ) be the space of all weakly compact operators. We denote space all operator ideals by O.
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Completely Simple Semigroups

Completely Simple Semigroups

Date: August 1968
Creator: Barker, Bruce W.
Description: The purpose of this thesis is to explore some of the characteristics of 0-simple semigroups and completely 0-simple semigroups.
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Completeness Axioms in an Ordered Field

Completeness Axioms in an Ordered Field

Date: December 1971
Creator: Carter, Louis Marie
Description: The purpose of this paper was to prove the equivalence of the following completeness axioms. This purpose was carried out by first defining an ordered field and developing some basic theorems relative to it, then proving that lim [(u+u)*]^n = z (where u is the multiplicative identity, z is the additive identity, and * indicates the multiplicative inverse of an element), and finally proving the equivalence of the five axioms.
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Completing the Space of Step Functions

Completing the Space of Step Functions

Date: August 1972
Creator: Massey, Linda K.
Description: In this thesis a study is made of the space X of all step functions on [0,1]. This investigation includes determining a completion space, X*, for the incomplete space X, defining integration for X*, and proving some theorems about integration in X*.
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A Computation of Partial Isomorphism Rank on Ordinal Structures

A Computation of Partial Isomorphism Rank on Ordinal Structures

Date: August 2006
Creator: Bryant, Ross
Description: We compute the partial isomorphism rank, in the sense Scott and Karp, of a pair of ordinal structures using an Ehrenfeucht-Fraisse game. A complete formula is proven by induction given any two arbitrary ordinals written in Cantor normal form.
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The Computation of Ultrapowers by Supercompactness Measures

The Computation of Ultrapowers by Supercompactness Measures

Date: August 1999
Creator: Smith, John C.
Description: The results from this dissertation are a computation of ultrapowers by supercompactness measures and concepts related to such measures. The second chapter gives an overview of the basic ideas required to carry out the computations. Included are preliminary ideas connected to measures, and the supercompactness measures. Order type results are also considered in this chapter. In chapter III we give an alternate characterization of 2 using the notion of iterated ordinal measures. Basic facts related to this characterization are also considered here. The remaining chapters are devoted to finding bounds fwith arguments taking place both inside and outside the ultrapowers. Conditions related to the upper bound are given in chapter VI.
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Concerning linear spaces

Concerning linear spaces

Date: June 1965
Creator: Gilbreath, Joe
Description: The basis for this thesis is H. S. Wall's book, Creative Mathematics, with particular emphasis on the chapter in that book entitled "More About Linear Spaces."
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Concerning Measure Theory

Concerning Measure Theory

Date: August 1972
Creator: Glasscock, Robert Ray
Description: The purpose of this thesis is to study the concept of measure and associated concepts. The study is general in nature; that is, no particular examples of a measure are given.
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Concerning the Convergence of Some Nets

Concerning the Convergence of Some Nets

Date: August 1964
Creator: Shaw, Jack V.
Description: This thesis discusses the convergence of nets through a series of theorems and proofs.
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Condition-dependent Hilbert Spaces for Steepest Descent and Application to the Tricomi Equation

Condition-dependent Hilbert Spaces for Steepest Descent and Application to the Tricomi Equation

Date: August 2014
Creator: Montgomery, Jason W.
Description: A steepest descent method is constructed for the general setting of a linear differential equation paired with uniqueness-inducing conditions which might yield a generally overdetermined system. The method differs from traditional steepest descent methods by considering the conditions when defining the corresponding Sobolev space. The descent method converges to the unique solution to the differential equation so that change in condition values is minimal. The system has a solution if and only if the first iteration of steepest descent satisfies the system. The finite analogue of the descent method is applied to example problems involving finite difference equations. The well-posed problems include a singular ordinary differential equation and Laplace’s equation, each paired with respective Dirichlet-type conditions. The overdetermined problems include a first-order nonsingular ordinary differential equation with Dirichlet-type conditions and the wave equation with both Dirichlet and Neumann conditions. The method is applied in an investigation of the Tricomi equation, a long-studied equation which acts as a prototype of mixed partial differential equations and has application in transonic flow. The Tricomi equation has been studied for at least ninety years, yet necessary and sufficient conditions for existence and uniqueness of solutions on an arbitrary mixed domain remain unknown. The domains ...
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